Many people who get dentures, braces such as Invisalign, and even veneers find that it affects their speech patterns, making them lisp or have trouble pronouncing words. Essentially what's happened is the inside architecture of their mouth has changed, and the tongue had completely adapted to the old architecture, and needs time to readapt.
If you experience a problem like this, and most people will with dentures, braces or a retainer, then here is a site that has a bunch of great tongue twisters that will retrain your tongue in a matter of a week or two. Pick ten or twenty of them and do them three times each, twice a day. You'll find yourself laughing and struggling at first, but these are used by actors all the time to refine their diction.
They are very clever, like "Six thick thistle sticks, six thick thistles stick," and even short, like "Unique New York." (Try that three times in a row!) Click here for the site.
If you're hesitating on getting dentures or braces because you're worried about how it will affect your speech, my advice is find a dentist that you love and trust. That way you'll make sure you have the best fit, and I guarantee you'll be glad you made the changes in the long run.