To find the coefficients \(a\) and \(b\), we expand \(\sqrt[3]{(1 + 9x)}\) using the binomial series for small \(x\):

\(\sqrt[3]{(1 + 9x)} = (1 + 9x)^{1/3} \approx 1 + \frac{1}{3}(9x) - \frac{1}{9}(9x)^2 + \frac{5}{81}(9x)^3\)

\(= 1 + 3x - 9x^2 + 45x^3\)

Comparing this with \(1 + 3x + ax^2 + bx^3\), we find:

\(a = -9\)

\(b = 45\)