Both are correct. "What kind of" expects one category ("What kind of music? — Jazz"); "what kinds of" invites several ("What kinds of music? — Jazz, rock and classical"). In casual speech "what kind of" covers both.
'What kind of' → one category expected.
'What kinds of' → several categories expected.
Speech: 'kind' covers both. Writing: use 'kinds' before lists.
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Both are correct — they ask different things.
What kind of expects one category: "What kind of music do you like?" — "Jazz."
What kinds of invites several categories: "What kinds of music do you like?" — "Jazz, rock and classical."
In everyday speech, what kind of is used for both — nobody will misunderstand you.