$\large\begin{aligned} f(x) = &x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}} + \dfrac{1}{x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}}}\\&+\dfrac{1}{x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}} + \dfrac{1}{x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}}}} \end{aligned}$

What is the smallest real value that the function $f$ can attain over all real values of $x ?$

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