If you're talking about DIY and not an official process per se (or "lobang"), it's more of a social skill than a technical skill, pretty boy.
Before the age of the internet, this would've been a hell of a task. Now, though, most of these producers have their own websites where they have either (1) an e-mail address to send e-mail to or (2) a feedback form (which gets sent to an e-mail address you're not supposed to know).
It's actually a fallacy that most of them are "busy people" and hence having no time to attend to e-mails from random individuals. They're not that evil and will spare a few seconds to scan through your message and respond if they think you deserve a reply. If they don't appear to have replied to the part about sharing the mix files with you, take it as a hint that they're unwilling to do so.
All you have to do is click on the "send" button. After that, cross your fingers. If you really want some concrete backing, let me just say that you have to know how to make the approach in writing. The choice of words, tone, and style all contribute to how seriously "busy" people will take you. A truely formal letter doesn't work all the time - you have to find a balance.