Balm Mushroom is a sell-only item in Generation V. It's a rare mushroom which gives off a nice fragrance. It cannot be sold in Poké Marts, but the Maid in the camper on Route 5 will pay 
25,000 for it. You can find it with the Dowsing Machine in Striaton City.
They can be obtained in X and Y from Restaurant Le Wow and can be sold at Poké Marts for 6,250.
In the demo of Pokemon Sun/Moon when you Celebrate the Birthday of the Pikachu, in the Town Hall, you obtain a Balm Mushroom that you can transfer over to the full version of the game.
Stub!
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