Let \( S \) be the region bounded by the curves \( y = x^{3} \) and \( y^{2} = x \). The curve \( y = 2|x| \) divides \( S \) into two regions of areas \( R_{1} \) and \( R_{2} \).
If \( \max\{R_{1}, R_{2}\} = R_{2} \), then \( \dfrac{R_{2}}{R_{1}} \) is equal to ______________.
