Welcome! Adding an example dataset to your question will help folks help you. It doesn't have to be your real data, just something similar that code can be run on. 
See some ideas on how to do this here.
That being said, it sounds like this could be a job for the emmeans package, although I'm not sure how/if this will work with your dummy coding rather than having your factors as factors. The package has a pretty thorough set of vignettes listed here that you may find helpful for getting started.
If working with factors you don't need to refit the model, but instead ask emmeans() for the comparisons you are interested in (ideally driven by the research question and not just a specific small p-value 
). The function will average over the variables that aren't of interest.
If you are interested all pairwise comparisons of factors you would do something like
emmeans(fit, pairwise ~ cCue:cGroup)
If you were interested in comparisons among, e.g., cCue within each cGroup you'd do
emmeans(fit, pairwise ~ cCue|cGroup)