What are the effects of salt additives and impurities on the CMC?
Every chemical present can interact with the free lipid and/or with the micelles. Organic chemicals will tend to interact with the lipophilic portion of the lipids, while ionic ones will interact with the polar head.

Depending on their structure, all those species can have a stabilizing or destabilizing effect on the formation of micelles and so the CMC will change accordingly.

Of particular importance is the "ionic strength" of the solution (you should research that term).