Did I do something wrong?

I had been working on Fermat's Last Theorem and decided to try this equation:

\(3987^{12} + 4365^{12}=n^{12}\).

Using a calculator, I got the value of \(n\) as \(4472\), which is impossible since Fermat's Last Theorem clearly states that \(x^n + y^n = z^n\) is not possible for any positive integer value of \(x, y\) and \(z\) provided that \(n > 2\). What did I do wrong?

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