Right triangular prism $ABCDEF$ has triangular faces $\triangle ABC$ and $\triangle DEF$, with edges $\overline{AD}$, $\overline{BE}$, and $\overline{CF}$. The angles are $\angle ABC = 90^\circ$ and $\angle EAB = \angle CAB = 60^\circ$. Given that $AE = 2$, the volume of $ABCDEF$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m + n$.

Let's think step by step and output the final answer within \boxed{}.
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