I just attempted to update my kernel from 4.2 to 4.6, in Ubuntu 14.04, on a Dell XPS 15 9550. I am interested in the improvements to USB-C support and "Dell laptop support improvements" in the 4.6 kernel.
I did so by downloading linux-headers-4.6.0-040600_4.6.0-040600.201606100558_all.deb, linux-headers-4.6.0-040600-generic_4.6.0-040600.201606100558_amd64.deb, and linux-image-4.6.0-040600-generic_4.6.0-040600.201606100558_amd64.deb from http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.6-yakkety/ into /tmp and running dpkg -i /tmp/*.deb. When I attempt to boot with the 4.6 kernel, it drops me into the initramfs BusyBox shell, with the error message ALERT! /dev/disk/by-uuid/1e4790ae-0501-4be4-b965-e2b7c77392eb does not exist. Dropping to a shell.
I found this similar question but couldn't use the information there to resolve this. Here's some info (blkid, /etc/fstab, fdisk -l, and /boot/grub/grub.cfg) that I believe might be helpful: (if something else would be useful, please let me know!)
17:52:11 ~ λ sudo blkid /dev/nvme0n1p1: LABEL="ESP" UUID="6441-2C20" TYPE="vfat" /dev/nvme0n1p3: LABEL="OS" UUID="8CFA6776FA675C08" TYPE="ntfs" /dev/nvme0n1p4: LABEL="WINRETOOLS" UUID="3072C71172C6DAAC" TYPE="ntfs" /dev/nvme0n1p5: LABEL="Image" UUID="9676C7B376C79283" TYPE="ntfs" /dev/nvme0n1p6: UUID="1e4790ae-0501-4be4-b965-e2b7c77392eb" TYPE="ext4" /dev/nvme0n1p7: UUID="5a41f7e3-23ba-4c8d-95cd-7cbfc6579720" TYPE="swap" 17:55:03 ~ λ cat /etc/fstab # /etc/fstab: static file system information. # # Use 'blkid' to print the universally unique identifier for a # device; this may be used with UUID= as a more robust way to name devices # that works even if disks are added and removed. See fstab(5). # # <file system> <mount point> <type> <options> <dump> <pass> # / was on /dev/nvme0n1p6 during installation UUID=1e4790ae-0501-4be4-b965-e2b7c77392eb / ext4 errors=remount-ro 0 1 # /boot/efi was on /dev/nvme0n1p1 during installation UUID=6441-2C20 /boot/efi vfat defaults 0 1 # swap was on /dev/nvme0n1p7 during installation UUID=5a41f7e3-23ba-4c8d-95cd-7cbfc6579720 none swap sw 0 0 17:55:08 ~ λ sudo fdisk -l WARNING: GPT (GUID Partition Table) detected on '/dev/nvme0n1'! The util fdisk doesn't support GPT. Use GNU Parted. Disk /dev/nvme0n1: 256.1 GB, 256060514304 bytes 255 heads, 63 sectors/track, 31130 cylinders, total 500118192 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x09e97f16 Device Boot Start End Blocks Id System /dev/nvme0n1p1 1 500118191 250059095+ ee GPT 17:55:18 ~ λ cat /boot/grub/grub.cfg [... elided ...] menuentry 'Ubuntu' --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-simple-1e4790ae-0501-4be4-b965-e2b7c77392eb' { recordfail load_video gfxmode $linux_gfx_mode insmod gzio insmod part_gpt insmod ext2 if [ x$feature_platform_search_hint = xy ]; then search --no-floppy --fs-uuid --set=root 1e4790ae-0501-4be4-b965-e2b7c77392eb else search --no-floppy --fs-uuid --set=root 1e4790ae-0501-4be4-b965-e2b7c77392eb fi linux /boot/vmlinuz-4.6.0-040600-generic root=/dev/nvme0n1p6 ro quiet splash nouveau.modeset=0 $vt_handoff initrd /boot/initrd.img-4.6.0-040600-generic } [...elided ...] 
linux-image-4.8.0-040800rc8-genericon Ubuntu 14.04 without any issues.)