A Pre-RMO question! -25

Geometry Level 2

In a rectangle $ABCD$ , $\overline{AB}=5cm,\overline{BC}=3cm$ . Points F and G lies on line segment $\overline{CD}$ such that $\overline{DF}=1cm,\overline{GC}=2cm$ . Lines $\overline{AF}$ and $\overline{BG}$ when joined and extended intersects at $E$ . If the area of $\triangle AEB$ is $\dfrac{m}{n}cm^2$ where $m\in Z^+;n\in Z^+;\gcd(m,n)=1$ then find $m+n$