The toilet water supply doesn't seem to have a nut at all and rotating it or turning it does nothing. Unsure how to remove this:
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Have you pulled that bevelled white cover back - there may be a nut under there... – Solar Mike Apr 13 at 19:46
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That valve seems to be of the variety where the supply line and stop-valve are a single integrated unit. In the foggy haze of past bad ideas, this was not uncommon (although most that I encounter are metal).
You will need to shut off the cold water supply and replace the valve and flex supply line...
