# 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 $$x$$.

×