Polynomials are not fun

Algebra Level pending

\({x,y,z}\) are numbers such that \(xyz=1\), \(xy+xz+yz=2\), and \(x+y+z=3\). If \(x,y\) and \(z\) are the roots of the cubic polynomial \(3n^3-an^2+bn-c=0\), what is \(a+b+c\)?

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