The touch of Madness

Algebra Level 5

\[\large \left (x^9+\frac{1}{x^9} \right)+\left(x^5+\frac{1}{x^5}\right)=7\left(x^7+\frac{1}{x^7} \right)\]

If a complex number \(x\) satisfy the equation above, find the positive value of \(\left(x+\dfrac 1 x\right)\).

This is one of my original Madness problems.
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