Did an even tighter connection last week in AKL.
Arriving from Tahiti on Air Tahiti Nui scheduled 12:10 and departing on CX 12:50 for HKG.

The Air Tahiti flight arrived 25 minutes early, had to wait 20 min for a gate and then stopped at the gate. Everybody got up and waiting for the door to open. Nothing happend for 10 min. Then the pilot announced hat everybody needs to sit down again since the plane has to be towed. Several minutes later (image me getting fairly nervous....) the plane was pushed back a few meters (the pilot stopped to close to the building and the jetway could not reach the door), then the jetway docked and the door opened.

Somebody from CX was already waiting for us and looking for us at the door of the plane, walked us over to the CX gate, issued bording passes, asked for the Bag tags, radioed down how our bags look.
No new security check, no immigration. It was less than 20 min between opening of the door of the first plane and closing of the door of the CX flight. And even the bags made it.

So you should have no problem at all connecting from CX to CX. It is the same plane, and you can check in right at the gate as soon as you deplane.