How to transfer my purchased songs form Super Junior Shake to my new iPhone 5?

I tried logging in to Dooub inc. On my new iPhone but it still won't let me play the songs that I purchased. I read in one place that I just have to go through the purchase process again but I won't be charged… I just don't want to do it in case I DO get charged because I don't have 6 dollars to waste -.- So if anybody knows a different way or if they have tried this before and it worked for them… Please help!

You won't get charged again if you're using the same Dooub account or Apple ID - whichever you used to buy the songs.

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