Let \(x, y, z\) be the real roots of the cubic equation

\[2u^3-799u^2-400u-1=0\]

and let \(\omega = \tan^{-1} x+\tan^{-1} y+\tan^{-1} z\). If \(\tan \omega = \frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, what is the value of \(a+b\)?

This problem is posed by Russelle G.

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