Not so Subtle Roots

Algebra Level 3

\[x^2+x+1 = 0 \]

The roots of the equation above are denoted by \(r \) and \(s\), while the roots of th equation below are denoted by \( r^3 \) and \(s^3 \).

\[ax^2+bx+c = 0 \]

What is the value of \( - \frac b a \)?

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