Let \triangle A B C be a triangle with A B=5, B C=8, and, C A=7. Let the center of the A-excircle be O, and let the A-excircle touch lines B C, C A, and, A B at points X, Y, and, Z, respectively. Let h_{1}, h_{2}, and, h_{3} denote the distances from O to lines X Y, Y Z, and, Z X, respectively. If h_{1}^{2}+h_{2}^{2}+h_{3}^{2} can be written as \frac{m}{n} for relatively prime positive integers m, n, find m+n.