We study the rheological properties of wormlike micellar aqueous solutions of an anionic surfactant potassium oleate containing solubilized 1-phenyldodecane. We show that upon increasing the amount of absorbed hydrocarbon the rheological behavior of semidilute micellar solutions changes drastically, showing a sequence of different regimes: (i) a "fast-breaking" entangled regime, when very long micellar chains form a network; (ii) an "unbreakable" entangled regime, when the shortening of the micelles leads to the decrease of their reptation time up to the values close to the breaking time; (iii) an unentangled regime (for the first time evidenced for wormlike micelles), where the micelles are so short that they cannot interlace. Within the entangled regime, an unusual rheological behavior has been discovered, probably characterized by the dominant role of end or bond interchange reactions or "breathing" modes, which leads to a novel hypothesis that hydrocarbon is distributed nonuniformly along the micellar length, thus increasing the probability of micellar breakage at certain points.