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)