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)