In triangle \(ABC\) the medians \(\overline{AD}\) and \(\overline{CE}\) have lengths 18 and 27, respectively, and \(AB = 24\). Extend \(\overline{CE}\) to intersect the circumcircle of \(ABC\) at \(F\). The area of triangle \(AFB\) is \(m\sqrt {n}\), where \(m\) and \(n\) are positive integers and \(n\) is not divisible by the square of any prime. Find \(m + n\).

(第二十届AIME1 2002 第13题)