AMC 12 2017b Problem 9

A circle has center $(-10,-4)$ and radius $13$. Another circle has center $(3,9)$ and radius $\sqrt{65}$. The line passing through the two points of intersection of the two circles has equation $x + y = c$. What is $c$?

\textbf{(A)}\ 3 \textbf{(B)}\ 3\sqrt{3} \textbf{(C)}\ 4\sqrt{2} \textbf{(D)}\ 6 \textbf{(E)}\ \frac{13}{2}