Put a couple rows of tape under the rail on the side of the cabinet, like the first picture.
Take a razor blade or razor knife, and hold it at an angle so it puts a small cut through the artwork, in an area *underneath* the side rail. This is done so if the adhesive still sticks in an area, the most that can be peeled is to the line you've cut. You know the rail will cover the side of the cabinet over the cut. This is shown in the 2nd picture.
Take a 1.5 inch putty knife and a dead blow hammer. Put the putty knife edge under the side rail, and tap the dead blow hammer upwards until it cuts through all the tape. Do this down the entire siderail. It'll take about 10 minutes per side to go from one end to the other. This is done in the 3rd picture.
I don't know if the terminology is the same overseas, a dead blow hammer is a hammer that is covered in rubber and if it scrapes the cabinet, it won't tear up the artwork, just leaves rubber that you can wipe off.
The end result is the 4th picture. Use whatever solvent or adhesive remover you use to remove the old tape.
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