are you sure it's just one plant? it doesn't look like one is growing on the other, it looks more like two seperate plants in one pot.
I would take it out of the pot, remove any roots that are brown and mushy, and check to see if the two growths are actually connected. if they're not, you can re-pot them seperately without any harm.
edward is right about it needing more humidity, but that doesn't mean you should leave it sitting in the tray of water. the idea is to set the pot above the tray of water, so that the water evaporating from the tray will keep the air humid.
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