Trying to find the conditional expected value of X when X + Y = m, and X, Y are both independent binomial random variables w/ parameters n & p

If X and Y are independent binomial random variables with identical parameters n and p, calculate the conditional expected value of X given X+Y = m.

The conditional pmf turned out to be a hypergeometric pmf, but I'm a but unclear on how to relate that back into finding E[X|X+Y=m]