Mock AIME 1 2006-2007 Problems/Problem 7

7. Let $\triangle ABC$ have $AC=6$ and $BC=3$ . Point $E$ is such that $CE=1$ and $AE=5$ . Construct point $F$ on segment $BC$ such that $\angle AEB=\angle AFB$ . $EF$ and $AB$ are extended to meet at $D$ . If $\frac{[AEF]}{[CFD]}=\frac{m}{n}$ where $m$ and $n$ are positive integers, find $m+n$ (note: $[ABC]$ denotes the area of $\triangle ABC$ ).