Solving for $x$ in $M ^ {M ^ M} = x ^ {1 / (x-1)}$ where $M = 5 ^ {\sqrt{5} / 10}$

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Methods used by analogy, for example $x ^ x = 3 ^ 3 \implies x = 3$,

Determine the value of $x$ in $$M ^ {M ^ M} = x ^ {1 / (x-1)}$$ if $M = 5 ^ {\sqrt{5} / 10}$.