Option (Mac) / Alt (Win) + Shift -drag to create copy of a layer mask while simultaneously inverting the mask.
I suppose that some of you are thinking, “Julieanne, you’ve posted this shortcut before”, but here’s the tip: if the mask’s Density or Feather slider has been altered from their defaults (of 100% and 0.0 px) using the Properties panel, this shortcut will not work.
With that said, you can still use the shortcut to duplicate the layer mask (Option (Mac) / Alt (Win) -drag the layer mask thumbnail in the Layers panel). Then, to invert the mask, click the Invert button in the Properties panel (or use the shortcut Command (Mac) | Control (Win) + I to invert).
Many thanks to Meredith for identifying the cause of the disabled shortcut!