SMO 2010 Junior Round 1 Question 32

Given that $ABCD$ is a square. Points $E,F$ lie on sides $BC,CD$ respectively such that $BE=CF=AB/3$. Let $G$ be the intersection of $BF$ and $DE$. If $[ABGD]/[ABCD]=m/n$ in lowest terms, find $m+n$, where brackets denote area.