We investigate correlated electronic transport in single-walled carbon nanotubes with two intramolecular tunneling barriers. We suggest that below a characteristic temperature the long-range nature of the Coulomb interaction becomes crucial to determine the temperature dependence of the maximum { G} of the conductance peak. Correlated sequential tunneling dominates transport yielding the power law { G}–1}$, typical for tunneling between the ends of two Luttinger liquids. Our predictions are in agreement with recent measurements. [math mode missing closing $]