Maximum Area of a Pentagon on a Parabola

On the parabola $ y = x^2 $, let $ A $ be the vertex at $ (0, 0) $, $ M $ be the point $ (-5, 25) $, and $ L $ be the point $ (5, 25) $. Let $ T $ lie on the parabolic arc $ \overgroup{MA} $ and $ P $ on the parabolic arc $ \overgroup{AL} $, such that $ MT = LP $ and $ TA = PA $. These five points form the vertices of a pentagon $ MTAPL $. What is the maximum possible area of this pentagon? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.