I don't think you have quite got the use of the word correct. Crack is not a reflexive verb. You could say 'Mariah Carey's voice cracked', but not that that she cracked it herself. It means that when she was singing, the sound suddenly changed, and sounded bad. It is similar to how boys' voices break when they are adolescent. Sometimes they break gradually, but sometimes they crack suddenly like that, often during speech.

The other possibility is that she has discovered how to use it properly. If I say "I finally cracked how to speak Russian" it means that I have conquered the language and am able to speak it adequately. This is quite an ambiguous phrase to use and the whole context would have to be looked at before an accurate answer could be given.

I think it means to start speaking / to say something / to show her voice (previously she kept silent); like with the book - to open the book and start studying.