Primes? Squares? Polynomials? Too easy!

Level pending

Let \( R \) denote the remainder when the largest root of the polynomial \( x^3 - 1032x^2 + 276267x - 5120540 \) is squared, then divided by 12.

\( \sqrt[3]{R} \) can be expressed as either one of \( a + bi, c + di, \) and \( e + fi \), where \( a, b, c, d, e, f \in \mathbb{R} \). Find the value of \( a + b + c + d + e + f \)?

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