In this investigation we focus on the problem of modelling the transport of the charged species (lithium ions) in electrolyte solutions with moderate and high salt concentrations (0.1M to >2M), and consider the Nernst-Planck equation as a model of such processes. First, using a combination of magnetic resonance imaging (MRI) and inverse modelling (IM) we demonstrate that at higher concentrations the Nernst- Planck equation requires negative transference numbers in order to accurately describe the concentration profiles obtained from experiments. The need for such a physically inconsistent constitutive relation indicates the loss of validity of the Nernst-Planck equation as a model for this process. Next we consider the formation of ion pairs and clusters as a possible effect responsible for the appearance of negative transference numbers and derive an extended version of the Nernst-Planck system which accounts for these additional species. However, a careful analysis of this model reveals that incorporation of ion-pairing effects into the modelling will not change the transference numbers inferred from the experimental data via inverse modelling. This demonstrates that physical effects other than formation of ion pairs and clusters must be incorporated into the Nernst-Planck model in order for it to correctly describe ion transport at higher salt concentrations. One prime candidate for such effects is the motion of the reaction surface resulting from dendrite growth.