In triangle A B C, let S be on B C and T be on A C so that A S \perp B C and B T \perp A C, and let A S and B T intersect at H. Let O be the center of the circumcircle of \triangle A H T, P be the center of the circumcircle of \triangle B H S, and G be the other point of intersection (besides H ) of the two circles. Let G H and O P intersect at X. If A B=14, B H=6, and H A=11, then X O-X P can be written in simplest form as \frac{m}{n}. Find m+n.