Advanced Number Theory · Superchallenge problem

In triangle $ABC$, point $D$ lies on $AB$ with $\tfrac{AD}{DB} = \tfrac12$ and point $E$ lies on $AC$ with $\tfrac{AE}{EC} = \tfrac12$. The ratio $\dfrac{[ADE]}{[ABC]} = \tfrac mn$ in lowest terms. Find $m + n$.