Determine the value of x if log (x^3 - 1) - log (x^2 + x + 1) = 1.

$\log (x^3 - 1) - \log (x^2 + x + 1) = 1$

$\log \left( \dfrac{x^3 - 1}{x^2 + x + 1} \right) = 1$

$\dfrac{x^3 - 1}{x^2 + x + 1} = 10^1$

$x^3 - 1 = 10(x^2 + x + 1)$

$x^3 - 1 = 10x^2 + 10x + 10$

$x^3 - 10x^2 - 10x - 11 = 0$

$x = 11$