I would like to select areas which are brighter than X (X is determined visually).
Select -> Color range -> Highlights selects very bright areas, but it has no adjustments and it doesn't include some brighter midtones.
Select -> Color range -> Sampled Colors doesn't work on black and white photo at all.
Is there another method?
Select your photo. Copy it on the clipboard.
Make a new layer, can be the photo itself or a pure color, that depends on what you need that for.
Make a layer mask and paste the same photo.
Modify the curves of the mask. Use the white point droplet and black point droplet. Depending on how close the values are you will have a more contrasted selection.
Done. That mask has the values you need.
Now you have the pixels above the cut off value remaining. If you like you can also adjust the light triangle downward to exclude values above a certain point.