I had the same issue with Google Play Music. It seems Opera doesn't include all the codecs that e.g. Chromium includes and cannot actually stream mp3 (on my PC). Here's what I did:
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install chromium-browser
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go to "/usr/lib/x86_64-linux-gnu/opera-developer/lib/" (or something else than "-developer" if you are running a different version)
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make a backup of "libffmpeg.so.33"
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copy "/usr/lib/chromium-browser/libs/libffmpeg.so" over the old "libffmpeg.so.33" in opera's folder
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restart opera
Annoying, but it worked for me...