Salt Glands (alternatively, hyper-efficient kidneys)
This is how animals IRL drink salt water and manage to not die. This is how saltwater crocodiles, sea turtles, seabirds, and the extinct mihirungs dealt with excess salt. That said, salt glands are pretty much unknown in mammals. This may not be because "they can't do it", but rather because they may not need to, mammalian kidneys are quite a bit more complex than reptilian or avian kidneys and may be able to perform the roles of salt excretion without the need for specialized salt glands. The loops of Henle in kangaroo rat kidneys are crazy long and allow them to extract all the water they need just from eating seeds.
In fact, wild Bactrian camels (but not domestic ones, for whatever reason) are capable of drinking saltwater with no ill effects. It's unclear if such adaptations are present in wider desert-dwelling mammals. Marine mammals are known to not need to drink fresh water but they supposedly get all the fresh water they need from the bodies of their fish prey. How marine herbivores like dugongs meet their water needs is unclear.
Also, camels do not store water in their humps. They store fat. Camels meet their water needs by having incredibly efficient kidneys, complex nasal turbinates, and other adaptations that allow them to reduce the amount of water they expel to very low amounts. But they still lose water over time, and eventually do have to drink, they cannot get all of their water from their food like kangaroo rats.