Two spheres with radii 36 and one sphere with radius 13 are each externally tangent to the other two spheres and to two different planes \mathcal{P} and \mathcal{Q}. The intersection of planes \mathcal{P} and \mathcal{Q} is the line \ell. The distance from line \ell to the point where the sphere with radius 13 is tangent to plane \mathcal{P} is \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.
