We report on the nonlinear shear rheology of wormlike micelles made of cetylpyridinium chloride (CP+,Cl-) and sodium salicylate (Na+,Sal(-)) diluted in 0.5 M NaCl-brine. A unique solution at concentration phi = 12% has been investigated (T = 20.3 degrees C). This strongly viscoelastic surfactant solution is an almost perfect Maxwellian fluid in the low-frequency range (omega < 100 rads(-1)). The stress relaxation function G(t) is decreasing monoexponentially as G(t) = G(0) exp(-t/tau(R)), where G(0) (=240 Pa) is the elastic plateau modulus and tau(R) (=1.0 s) the terminal relaxation time. The fundamental feature of the nonlinear rheology is the evidence of a constant and robust stress plateau (no hysteresis) above a characteristic strain rate labeled (gamma) over dot I/N ((gamma) over dot I/N = 0.9 +/- 0.05 s(-1)). The solution at phi = 12% was selected because recent flow birefringence experiments revealed that the stress plateau mentioned previously is associated with a nonhomogeneous flow. Two phases of different birefringence and submitted to different velocity gradients have been clearly evidenced in the plateau region. Here we focus on the time dependence of the stress in start-up experiments. Varying the shear rate ((gamma) over dot = 0.05-10 s(-1)), we have identified three time ranges corresponding to three kinds of responses of the entangled network of wormlike micelles. At very short time (t much less than tau(R)), the wormlike micelles reacts as an elastic solid. At times of the order of tau(R) occurs the purely mechanical response of the system. The associated stress as a function of shear rate is interpreted in terms of mechanical instability. Remarkably, this regime exhibits strong similarities with that of conventional polymers : stress overshoot around t similar to tau(R) and damped oscillations at high strain rates. On the long-time scale (t much greater than tau(R)) and for (gamma) over dot > (gamma) over dot I/N, the system undergoes the transition toward a strongly inhomogeneous flow, which can be ascribed to the isotropic/nematic shear-induced transition. The present findings suggest finally that, in wormlike micellar solution, the purely mechanical instability does exist but is preempted by the transition toward an (nematic) inhomogeneous now.