I haven't gone back to Australia or I haven't been back to Australia
AHD "be", def. 4. "4.
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AHD "be", def. 4. "4. To go or come: Have you ever been to Italy? Have you been home recently?"
The two sentences can be equivalent. The first can imply permanence:
Jack (on the phone): When you moved to Azerbaijan from Perth, you said it would be for only a year.
Jill: Yeah, but I decided to stay longer. I haven't gone back to Australia.
If Jill had used "been"