Credibility of the source has long been known to be an important factor in persuading people to act in a certain way. The classic experiment was carried out by Hovland and Weiss (1951). The study showed participants articles about topics they were unlikely to hold a lot of information about (for example atomic submarines and anti-histamines. Participants were told these articles either came from high credibility sources (e.g. The New ~England Journal of Biological & Medicine) or low credibility sources (e.g. Pravda, a Soviet news magazine). As the figure below (taken from the original Hovland & Weiss, 1951, article) shows, high credibility sources were shown to cause much more change in attitude than low credibility sources were. This would suggest that Sensodyne were right to have a dentist advertise their product, as people are more open to having their opinions changed by a high credibility source. This has been explained through the mechanism of informative social influence, which explains people's conformity through the desire to hold the right opinion. We believe credible sources are more likely to be right than we are, so we change our opinions to be in line with theirs.
However, the advert may not be as persuasive as Sensodyne had hoped because, as can be seen in the diagram, the effectiveness of the high credibility source in maintaining people's attitude change over time is not as good as that of a low credibility source. For the sake of Sensodyne, I hope most people buy their toothpaste at more than month intervals!
Hovland, C. I., & Weiss, W. (1951). The influence of source credibility on communication effectiveness. Public Opinion Quarterly, 15, 635-650.