When the blockage has been successfully moved, you should see a drop in the water height. Check the drain is running by throwing down a bucketful of water. Rinse all the equipment thoroughly in fresh water and bind the rods together before storage.
If the drain remains blocked you may need the assistance of a professional. They will likely use a camera to ascertain the cause of the blockage; it may be that the pipe has collapsed due to subsidence. They will have a range of powerful tools to clear any stubborn blockages, e.g. high pressure water jetting.
If you fat deposits are visible on the plunger, a build-up of fat or grease may have been the cause of the blockage. Flush hot soapy water down the drain to help remove any deposits.