In triangle A B C, the medians \overline{A D} and \overline{C E} have lengths 18 and$ 27 , respectively, and A B=24. Extend \overline{C E} to intersect the circumcircle of A B C at F. The area of triangle A F B 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.