Question 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 $m + n.$