Problem by Lee Dongheng

Algebra Level 3

\[\large \begin {cases} x^\frac{1}{2}+y^\frac{2}{3}=8\\x+y^\frac{4}{3}=32\end {cases} \]

Let \(x\) and \(y\) be numbers satisfying the system of equations above, enter your answer as the sum of all possible values of \(y\).

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