In a class of extensions of the minimal supersymmetric standard model with (B-L)/left-right symmetry that explains the neutrino masses, breaking R-parity symmetry is an essential and dynamical requirement for successful gauge symmetry breaking. Two consequences of these models are: (i) a new kind of R-parity breaking interaction that protects proton stability but adds new contributions to neutrinoless double beta decay and (ii) an upper bound on the extra gauge and parity symmetry breaking scale which is within the large hadron collider (LHC) energy range. We point out that an important prediction of such theories is a potentially large mixing between the right-handed charged lepton ($e^c$) and the superpartner of the right-handed gauge boson ($widetilde W_R^+$), which leads to a brand new class of R-parity violating interactions of type $widetilde{mu^c}^dagger u_mu^c e^c$ and $widetilde{d^c}^daggeru^c e^c$. We analyze the relevant constraints on the sparticle mass spectrum and the LHC signatures for the case with smuon/stau NLSP and gravitino LSP. We note the smoking gun signals for such models to be lepton flavor/number violating processes: $ppto mu^pmmu^pm e^+e^-jj$ (or $tau^pmtau^pm e^+e^-jj$) and $pptomu^pm e^pm b bar{b} jj$ (or $tau^pm e^pm b bar{b} jj$) without significant missing energy. The predicted multi-lepton final states and the flavor structure make the model be distinguishable even in the early running of the LHC.
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