The \(x^\text{th}\) root of \(x\)

Let \(f: \mathbb Q^+ \to \mathbb R^+ \), we define \(f(x) = \sqrt[x]{x} \).

Let \(x\) and \(y\) be positive rational numbers such that \(x<y\) and \(f(x) = f(y) \). Find the sum of all possible values of \(x\).

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