\[\large ( a + b\omega + c\omega^{2})^{3} +(a + c\omega + b\omega^{2})^{3}=0\]

If \(a,b\) and \(c\) are distinct integers in a geometric progression which satisfy the equation above where \(\omega\) is a non-real cube root of unity, what is the least possible value of \(|a| + |b| + |c|\)?

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