There is a bus service that will take you north to Huay Xai and minivans or buses to either Chiang Mai or Chiang Rai (both have Air Asia flights to Bangkok) from Chiang Khong on the Thai side of the border. There is also a high season bus/minivan service directly from LPB to Chiang Mai, but as John says, you are looking at a very long journey, slow boat best part of 2 days to the border and bus one very long one to the border. If you need to save money I would take the bus south to Vientiane, cross the border there and get another bus back to Bangkok from Udon Thani, you could also get a train or there are flights from Udon too.
Other option is to go to Vientiane and then down to udon Thani. However just make sure you add up your boat, bus and accom prices ad it may still be cheaper to fly from luang prabang back to bangkok
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