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.