A tricky area

Calculus Level 4

Let \(a\) be a positive constant such that the area enclosed by the curve \(x^{2/5} + y^{2/5} = a^{2/5} \) can be written as \( \dfrac AB \pi a^2\), where \(A\) and \(B\) are coprime positive integers.

Find the sum of digits of \(A+B\).

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