Python 3.8, 41 bytes

lambda l:[t:=sum(l[:len(l)//2]),sum(l)-t] 

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Straightforward solution. Takes in a list, and returns the list of left and right sum.

Python 3.8, 41 bytes

lambda l:[t:=sum(l[:len(l)//2]),sum(l)-t] 

Try it online!

Straightforward solution. Takes in a list, and returns the list of left and right sum.

Interesting idea that didn't go anywhere :(

Python 3, 45 bytes

lambda l,t=1j:l>[]and l[-1]+t*f(l[-2::-1],-t) 

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Returns a+bj where a, b is the right and left sum respectively.