In triangle \(ABC\), \(AB=13\), \(BC=15\) and \(CA=17\). Point \(D\) is on \(\overline{AB}\), \(E\) is on \(\overline{BC}\), and \(F\) is on \(\overline{CA}\). Let \(AD=p\cdot AB\), \(BE=q\cdot BC\), and \(CF=r\cdot CA\), where \(p\), \(q\), and \(r\) are positive and satisfy \(p+q+r=2/3\) and \(p^2+q^2+r^2=2/5\). The ratio of the area of triangle \(DEF\) to the area of triangle \(ABC\) can be written in the form \(m/n\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m+n\).
(第十九届AIME1 2001 第9题)