Devilish fun

Algebra Level 4

The product of the real roots of the polynomial

\[ f(x) = x^4 - 4x^3 + 6x^2 -4x-666 \]

can be written as \(a - \sqrt{b}\), where \(a\) and \(b\) are positive integers. What is the value of \(a+b\)?

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