Quadratic Duos

Algebra Level pending

\[ (x^2-2mx - 4(m^2+1))(x^2-4x-2m(m^2+1)) = 0 \]

Find all real numbers \(m\) such that the equation above has exactly three different roots. Input your answer as the sum of all possible values of \(m\).

This problem is not written by me.
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