Let the polynomial \(x^{2}+x+1\) have roots \(\alpha\) and \(\beta\). Then there exists a polynomial with the roots \(\alpha^{2}\) and \(\beta^{2}\) in the form of \(ax^2+bx+c\), where \(a\), \(b\) and \(c\) are all integers, with \(a\) begin positive and \(\gcd(a,b,c) = 1 \).

Find \(a+b+c\).

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