The touch of Madness

Algebra Level 5

(x9+1x9)+(x5+1x5)=7(x7+1x7)\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 xx satisfy the equation above, find the positive value of (x+1x)\left(x+\dfrac 1 x\right).

This is one of my original Madness problems.
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