-(으)ㄴ 적 is a past occasion, so with 많다 it means having done something plenty of times: 저도 해본 적 많아요 'I've tried it lots', 방송하다가 실수한 적 많아요 'I've slipped up on air plenty of times'. The textbook forms 적 있다 and 적 없다 ask whether you have ever done it at all; adding 많다 answers with quantity. Every line here is relaxed conversation.