Almost Quartic Equation

Algebra Level 4

If one of the root of the equation \(x^3+x^2+x+1 = 20^2\)

can be expressed as \(-a-i\sqrt{b}\) for positive integers \(a,b\)

What is the value of \(a+b\)?

Details and Assumptions:

\(i = \sqrt{-1}\)

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