Let \( a \) and \( b \) be two nonzero real numbers. If the coefficient of \( x^5 \) in the expansion of \( \left(a x^2 + \frac{70}{27 b x}\right)^4 \) is equal to the coefficient of \( x^{-5} \) in the expansion of \( \left(a x - \frac{1}{b x^2}\right)^7 \), then the value of \( 2b \) is _____.
