In quadrilateral $$ABCD$$, $$\angle{BAD}\cong\angle{ADC}$$ and $$\angle{ABD}\cong\angle{BCD}$$, $$AB = 8$$, $$BD = 10$$, and $$BC = 6$$. The length $$CD$$ may be written in the form $$\frac {m}{n}$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m + n$$.

(第十九届AIME2 2001 第13题)