Do you actually have music on the Maxell CD-R? That is, you can put it into a CD player (not MP3 player) and it'll play music?
If so, then it can't be used to record data. The CD-R data and music formats are different, and you can't mix the two.* I'm not even sure you can add additional music to a music CD. If I remember right, the music is written as one continuous data stream. (Which is how you can have one song lead directly into another even though they have their own index markers, like the opening of the Beatles' Sgt. Pepper leads directly into With a Little Help from My Friends without any pause.)
* There was a special hybrid format, where half the CD is used for music and the other half for data. But you had to format the CD this way before you wrote anything to it.