A particle of mass \(m\) moves along the \(x\)-axis in a region where its potential energy is given by \(U(x) = U_0\left[\left(\dfrac{x}{b}\right)^2 - \dfrac{1}{3}\left(\dfrac{x}{b}\right)^3\right]\), where \(U_0\) and \(b\) are positive constants.

Particle 1 is released from rest at \(x = -b\), and an identical Particle 2 is released from rest at \(x = +b\). What is the ratio of the maximum speed of Particle 1 to the maximum speed of Particle 2, \(\dfrac{v_{1,\text{max}}}{v_{2,\text{max}}}\)?