Let \( \displaystyle \alpha = \max_{x \in R} \{8^{2 \sin 3x} \cdot 4^{4 \cos 3x}\} \text{ and } \beta = \min_{x \in R} \{8^{2 \sin 3x} \cdot 4^{4 \cos 3x}\} \). If \( 8x^{2} + bx + c = 0 \) is a quadratic equation whose roots are \( \alpha^{1/5} \) and \( \beta^{1/5} \), then the value \( c - b \) is equal to:
