Christmas Contest - Guts Round - Set 1 Problem 2

Let $ABCD$ be a unit square and $E$ be a point in $ABCD$ such that $\triangle ABE$ is an equilateral triangle. If $\frac{\sqrt m}{n}$ is the ratio of the areas of $ABE$ and $ABCD$, where $m$ and $n$ are positive integers with $m$ not divisible by the square of any prime, compute the value of $m+n$.