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 \(\tfrac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n\).