I often see good players note on their convention cards that 1NT may contain a 6 card minor. Depending on the strength on the 1NT range, I would bid such hands 1m - 2m (12-15) or 1m - 3m (15-18). What are the benefits of opening 1NT with 6 card minor? What are the characteristics of such hands?
To expand on the answer by ruds, the scoring also plays into the decision.
Where as it requires 10 tricks in a Major suit to make game, and 11 in a Minor, it takes only 9 tricks to contract for game in Notrump. This makes the required total strength required for a good shot at game about 4 Points less in Notrump (~25 combined HCP) than in the minor suit (~29 combined Points).
On distributional hands the additional strength can be available outside the high card strength, and leverage trump length to protect against an opponents length tricks in a side suit. When the hands are balanced, it is usually wiser to play for the reduced total required tricks.
The main advantage of opening 1NT is that it limits the hand in both in terms of strength and distribution. When you open 1 minor, you can have between 3 and 7 cards in the suit, between 10 and 20something HCP and can be void in any suit. When you open 1 NT, your hand is limited in strength and the distribution is well defined. This is a huge advantage if the bidding turns competitive and a large advantage in partnership bidding (just one example: responder, with a 6-card major and game-going strength, can safely place the contract, knowing that opener has at least adequate support).