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Liquid crystal elastomers (LCEs) are a class of smart elastomers exhibiting unusual mechanical behavior, including large energy dissipation and soft elasticity under uniaxial tensile loading. LCEs are composed of liquid crystal molecules, called mesogens, linked by a network of polymer chains. During deformation, the mesogens orient in the direction of the loading, leading to soft elasticity, which is an increase in strain at constant stress. The combination of mesogen rotation and intrinsic polymer viscoelasticity leads to a nonlinear viscoelastic soft elastic behavior. The aim of this paper is to investigate the coupling between the viscoelastic mechanisms and soft elasticity in main chain LCEs. We propose a rheological model in which the mesogen rotation during deformation is represented by a reversible slider while viscoelastic relaxation mechanisms are modeled as series of Maxwell elements coupled or decoupled with mesogen rotation. Fitting this model to experimental data demonstrate that the coupling between polymer chain viscoelasticity and mesogen rotation is partial, i.e. the long-time relaxation mechanisms are coupled and the short-time relaxation mechanisms are decoupled from mesogen rotation. Furthermore, we show that the viscosity of mesogen rotation is not necessary to properly predict the elastic modulus during the soft elasticity but it is needed to properly predict the initiation of the phenomenon. \end{abstract}