Suppose that \(a, b, c\) are positive reals such that
\[\begin{align}
& x^3+7x^2+24x+18 \\
&= (x+a)(x+b+ci)(x+b-ci),
\end{align} \]
where \(i\) is the imaginary number that satisfies \(i^2=-1.\) What is the value of \(a+b+c?\)

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