The reason given for waiting 6 hours after meat is since some of the meat may be stuck in your teeth. If someone uses dentures, and has two pairs - one for meat and one for dairy - would they still have to wait? (sources)
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As @Vram mentioned, per Rashi on Hullin 105a DH "Asur Le'echol Gevinah" the reason for the six hour break: is the taste of meat lingering in the throat. Even if you took teeth out of the picture, you still have the lingering taste and should still wait the six hours.
See Taz 89:1 or Shach :2 that two reasons apply to waiting, and we wait when either reason applies: that food may be stuck in the teeth, and that the taste of swallowed meat lasts. Thus, assuming you swallowed meat (not merely chewed it and spat it out), you'd need to wait thereafter. If you chewed and spat out the food and then changed your dentures, neither reason would seem to apply, so I doubt you'd need to wait. Obviously, don't rely on my reasoning if this question is practical for you: consult your rabbi.