Let \(f(x)\) be a polynomial with integer coefficients such that

\[ \begin{align*} f(1) &= 1 \\ f(2) &= 8 \\ f(3) &= 27 \\ f(5) &= 125 \\ f(6) &= 216 \\ f(7) &= 343. \end{align*} \]

What is the minimum possible value of \(|f(4)|?\)

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