is this sentence correct? "Sue works the hardest of all students"

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the sentence is fine
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I think you need an article before "students."

She works the hardest of all the students. She works the hardest of all my students.
all students = on earth

all the students = in our school, in our city, who have participated, etc.

I would say the determiner changes the meaning of the sentence.
yes, the is required in this context
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