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)