After following a subset of this advice, this is how I got the Python GDAL 1.11.0 install to work on Ubuntu 14.04 with pip:
Install dependencies:
sudo apt-get install libgdal-dev libgdal1h
Pip install and pass along the include path:
sudo pip install --global-option=build_ext --global-option="-I/usr/include/gdal" gdal