Solve equation for $x$, why not a closed format?

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I am trying to solve for $x$ the following:

$\big(\frac{x-m}{d*x+f}+1\big)^s = \big(\frac{n-m}{d*x+f}+1\big)$

I have tried with Wolfram Alpha functionality Solve but I didn't obtain anything. Is there a way to solve it or proof that it can not be solved analytically?