Red eared slider with snails?!?

hey i have a res turtle that i keep in a huge plastic tub the turtle is happy he has every thing he needs in there. the tub doesn't have a filter like a fish tank would so i clean it when necessary but in sick of the algae. its in the tank, on the tank, on the turtle! everywhere. its not a problem for the turtle but it is for me. i remember working at Walmart in the pets area an we had these algae eating snails i forgot the name of the snails but all they did was eat algae an multiply. lol so i was wondering would they live well with turtles i know my turtle would just swallow the baby's so in thinking i get out the 10 gallon an when i see baby's id get them out an grow them in the 10 gallon until they big enough idk will this work? my turtle is about 5''(in) plus would he eat the snails. will the snails live in the tub with no filter? HELP!