jmc

From the problem, we can see that $XZ=ZY$ and $XZ+ZY=XY$, which means that $X,$ $Y,$ and $Z$ form a degenerate triangle. In other words, $Z$ is the midpoint of $XY$. Since from Y to Z, we go 2 steps left and 14 steps down, we do the same to arrive at $X=(-1-2,-7-14)=(-3,-21).$ Therefore, the sum of the coordinates of $X$ is $\boxed{-24}.$