There's no image link to your question here on ifixit
Are you sure that the 5V - 1A doesn't mean that it the specification required for the power adapter that is connected to the beatsX?
It's not unusual for the adapter voltage specs to be shown on a device near where it is plugged in.
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Use this [https://www.youtube.com/watch?v=zg9k4c1WeRk|video] to open it up and check what it says on the battery itself. Then use that information to search for suppliers.
@jannekehart
There's no image link to your question here on ifixit
Are you sure that the 5V - 1A doesn't mean that it the specification required for the power adapter that is connected to the beatsX?
It's not unusual for the adapter voltage specs to be shown on a device near where it is plugged in.