A system for successively uncovering a plurality of contiguous ports in a tubing liner within a wellbore, or for successively uncovering individual groups of ports arranged at different but adjacent locations along the liner, to allow successive fracking of the wellbore at such locations. Sliding sleeves in the tubing liner are provided, having a circumferential groove therein, which are successively moved from a closed position covering a respective port to an open position uncovering such port by an actuation member placed in the bore of the tubing liner. Each actuation member comprises a dissolvable plug which in one embodiment is retained by shear pins at an uphole end of a collet sleeve, the latter having radially-outwardly biased protuberances (fingers) which matingly engage sliding sleeves having cylindrical grooves therein, based on the width of the protuberance. In one embodiment, when actuating the most downhole sleeve, the shear pin shears allowing the plug to move in the collet sleeve and prevent the protuberance (fingers) from disengaging.