# Okay, That's A Lot Of Integers

$x+y+z=3$ $x^3+y^3+z^3=3$ Let $$\displaystyle a$$ be the sum of all possible integer values of $$\displaystyle x$$.

Let $$\displaystyle b$$ be the sum of all possible integer values of $$\displaystyle y$$.

Let $$\displaystyle c$$ be the sum of all possible integer values of $$\displaystyle z$$.

Find $$\displaystyle a+b+c$$.

Details and Assumptions:

All the possible values of $$x,y,z$$ are to be summed,not only the possible distinct values of $$x,y,z$$.For example, if the solutions were $$(1,2,3)$$ and $$(1,2,4)$$,then the answer would be $$1+1+2+2+3+4=13$$

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