There are ways to do it but probably not so easy and quite expensive or labor intense.
Look for various solvents that have different solubility for sodium chloride and sodium nitrate. Different temperatures or pH can also help separate two salts.
A good video on how to do chemical extraction is https://www.youtube.com/watch?v=NffmujESqNw It was made by NileRed and I highly recommend his videos if you are interested in chemistry in general, a lot of methods are demonstrated in his videos.
Other chemical youtubers to watch is NurdRage doing a re-crystallization to increase purity https://www.youtube.com/watch?v=uVA0rK_VITY
or Dough's Lab where he uses pH to affect solubility to separate chemicals https://www.youtube.com/watch?v=C31AKmRi69Q
One way to get pure sodium nitrate would be to add silver nitrate to the solution, silver ions react with the chloride and precipitate out as silver chloride, leaving sodium nitrate in solution. By being careful with how much silver nitrate is added, a re-crystallization of the solution could remove most of the contaminants in a following step. This procedure converts sodium chloride to sodium nitrate.
I'm not claiming it is a good procedure, but it could be done in that way.
Göran
