Removing bathroom cabinet-floor to ceiling, wedged in

Is your TT aluminum clad on wood frame?

If so, cabinets are fastened with wood screws from outside the frame before putting alum claddings on.

I did a similar repair once. I located the screws and use a small cutting disc on a power drill to cut off the screws close to the base and push the frame away from the cabinet. There should be enough flexibility in the frame to free up the cabinet.