Let $$R = (8,6)$$. The lines whose equations are $$8y = 15x$$ and $$10y = 3x$$ contain points $$P$$ and $$Q$$, respectively, such that $$R$$ is the midpoint of $$\overline{PQ}$$. The length of $$PQ$$ equals $$\frac {m}{n}$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m + n$$.

(第十九届AIME2 2001 第4题)