First item is that this company who dumped this soil on your tree did a very naughty and irresponsible thing. Make sure you report this to that company. These drivers are taught HOW and WHERE to dump and they messed up big time.
Apart from having this company replace your flowering cherry tree, I would get duct tape and wrap a few wrappings tightly to pull the trunk split together.
You do not want to allow these wrappings to be on very long at all. In fact, I would take that duct tape and where it contacts the bark add a layer of thin felt to be between the bark and the tape. That will help when you remove this taping which should only happen when that gap has been closed by the plant itself.
Not a procedure to do and forget about. Please send a picture because I am just assuming stuff based on my own imagination from what you've said.
Those that sell gravel and soil and mulch and rock...need to have repeat business. To dump their load on your little cherry tree was just wrong. Take pictures, write down the dates, times, any names and then try to pull this split trunk back together. Include the time you spend trying to mend your tree. Call your Cooperative Extension Service for help and opinion.
The important part of this trunk is a thin thin cambium layer beneath the bark. Your tree has only been compromised at two places; one either side of the tree at the bottom of the split. Trees encapsulate and protect themselves when this happens in nature. Your tree might be able to live but not thrive. I would maximize the success rate by pulling the trunk together allowing the tree to knit the cambium together using the duct tape. Use a mesh fabric beneath the sticky part of the tape.