2017 AMC 12B 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\qquad\textbf{(B)}\ 3\sqrt{3}\qquad\textbf{(C)}\ 4\sqrt{2}\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ \frac{13}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.