Minimize it!

Algebra Level 3

(x+1x)6(x6+1x6)2(x+1x)3+(x3+1x3)\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 xx is a positive real number, find the minimum value of the expression above.

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