2002 AIME I Problem 13

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$.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.