Sum of Powers is Perfect Square

\(Q\), \(X\), \(Y\) and \(Z\) are \(4\) positive integers where:

\(Q={ 3 }^{ X }+{ 5 }^{ Y }+{ 7 }^{ Z }\)

\(Q \) is a perfect square. Find \(X+Y+Z\), and \(Q\) is the minimum possible perfect square in the sum above.

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