TR-MO-R1 2018 Problem 22

$m$ ve $n$ tam sayılar olmak üzere, $(m+n^2)(m+1) = 4mn$ eşitliği sağlanıyorsa $m+n$ ifadesinin alabileceği farklı değerlerin toplamı kaçtır?

a) $-2$ b) $-1$ c) $0$ d) $1$ e) $2$

Official text Turkish Mathematical Olympiad, first round 2018 official paper, page 8. Quoted with source.

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