In quadrilateral $$ABCD, BC=8, CD=12, AD=10,$$ and $$m\angle A= m\angle B = 60^\circ.$$ Given that $$AB = p + \sqrt{q},$$ where $$p$$ and $$q$$ are positive integers, find $$p+q.$$

(第二十三届AIME1 2005 第7题)