In triangle \(ABC, AB=13, BC=15,\) and \(CA = 14.\) Point \(D\) is on \(\overline{BC}\) with \(CD=6.\) Point \(E\) is on \(\overline{BC}\) such that \(\angle BAE\cong \angle CAD.\) Given that \(BE=\frac pq\) where \(p\) and \(q\) are relatively prime positive integers, find \(q.\)

(第二十三届AIME2 2005 第14题)