Inspired by Calvin Lin - Part II

Algebra Level 5

\[ f(n)=x^2 + ( x -1) ^2 +(x+2)^2+\ldots+(x-2n+1)^2+(x+2n)^2 \]

As \(x\) ranges over all real values, If the minimum value of \(f(n)\) is \( \dfrac{3936170}{59} \) for some natural number \(n\), find the value of \(n\).

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