# Simultaneous 3 Variables

Solve for integers a, b, c:

$a+b=1-c$ $a^{3}+b^{3}=1-c^{2}$

If the solutions you obtain for example, (1,2,3) and (4,5,6) then your answer will be $$1+2+3+4+5+6 = \boxed{21}$$.

Disregard the solution family: $$(m, -m, 1)$$.

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