  We construct a full left-right model for the electroweak interactions based
on the $SU(3)_{L}\otimes SU(3)_{R}\otimes U(1)_{X}$ gauge symmetry. The fermion
content of the model is such that anomaly cancellation restricts the number of
families to be a multiple of three. One of the most important features of the
model is the joint presence of three light active neutrinos, three additional
neutrinos at keV mass scale, and six heavy ones with masses
around\textbf{$10^{11}$} GeV. They form a well-motivated part of the spectrum
in the sense they address challenging problems related to neutrino oscillation,
warm dark matter, and baryogenesis through leptogenesis.
