If the plunger fails, this is the tool you need before calling a professional. It is a flexible metal cable with a corkscrew tip, housed in a rigid plastic tube.
Since you haven't specified a particular product (like a specific plunger, drain snake, or chemical cleaner), I have reviewed the three main methods of unblocking a toilet. unblock a toilet
Once you hit resistance, rotate the crank to either hook into the obstruction (like a wet wipe) or break it apart (like organic matter). If the plunger fails, this is the tool
Put on long, heavy-duty rubber gloves and safety eyewear to protect against bacteria and wastewater splashback. Phase 2: How to Unblock a Toilet Using Tools If the plunger fails
