Change your database 🙂
Instead of having students be a multi-valued field, have a students table. Now, a sport can involve multiple students, and a student can play multiple sports. To represent this many to many relationship, create a third table, thus:
Table: sports
Fields: id, name
Table: students
Fields: id, name
Table: students_sports
Fields: sport_id, student_id
Now, getting all unique students is just a matter of:
SELECT name FROM students;