Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos \left( \frac{x}{3} - x \right) \cdot \cos \left( \frac{x}{3} + x \right) \cdot \sin 3x \cdot \cos 6x, x \in \mathbb{R} \] be \([\alpha, \beta] \). Then the distance of the point \((\alpha, \beta)\) from the line \(3x + 4y + 12 = 0\) is