Solve the equation $f(x)=\sum_{n=x}^{10}\sqrt[|n-2|+1]{n\log_{2}(n)}$ for $x$ in $f(x)=7.5?$

Question

Given the following equation

$$f(x)=\sum_{n=x}^{10}\sqrt[|n-2|+1]{n\log_{2}(n)}$$

How could I go about solving for $x$ in $f(x)=7.5$ for example (or to show that no such $x$ exists)? Or, really for any value of $f(x)$?

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