Question 13
Let $ABCDE$ be a convex pentagon with $\overline{AB} \parallel \overline{CE},$ $\overline{BC} \parallel \overline{AD},$ $\overline{AC} \parallel \overline{DE},$ $\angle ABC = 120^\circ,$ $AB = 3,$ $BC = 5,$ and $DE = 15.$ Given that the ratio between the area of triangle $ABC$ and the area of triangle $EBD$ is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers, find $m + n.$