Let \triangle T B D be a triangle with T B=6, B D=8, and D T=7. Let I be the incenter of \triangle T B D, and let T I intersect the circumcircle of \triangle T B D at M \neq T. Let lines T B and M D intersect at Y, and let lines T D and M B intersect at X. Let the circumcircles of \triangle Y B M and \triangle X D M intersect at Z \neq M. If the area of \triangle Y B Z is x and the area of \triangle X D Z is y, then the ratio \frac{x}{y} can be expressed as \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.