Point $$P_{}$$ is located inside triangle $$ABC$$ so that angles $$PAB, PBC,$$ and $$PCA$$ are all congruent. The sides of the triangle have lengths $$AB=13, BC=14,$$ and $$CA=15,$$ and the tangent of angle $$PAB$$ is $$m/n,$$ where $$m_{}$$ and $$n_{}$$ are relatively prime positive integers. Find $$m+n.$$

(第十七届AIME1999 第14题)