A pentagon $ABCDE$ is formed by three triangles: $△ABC$, $△ACD$, and $△ADE$. Given that $AB=BC=3$, $AE=ED=3$, and $CD=2$. The diagonal lengths are $AC=4$ and $AD=4$. The area of pentagon $ABCDE$ can be written as $\sqrt{m}+\sqrt{n}$ where $m$ and $n$ are positive integers. What is $m+n$?