Minimize it!

Algebra Level 3

$\large \frac { {\left( x + \dfrac{1}{x} \right)}^{6} - \left( x^6 + \dfrac{1}{x^6} \right) - 2}{ {\left( x + \dfrac{1}{x} \right)}^{3} + \left( x^3 + \dfrac{1}{x^3} \right)}$

Given that $x$ is a positive real number, find the minimum value of the expression above.

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