If the plunger fails, you need a toilet auger (also called a closet auger). This is a flexible metal cable with a crank handle.
Bleach is primarily a disinfectant, not a drain cleaner. Its effectiveness depends entirely on what is causing the blockage: does bleach unblock toilet
Before pouring bleach down your "throne," consider these serious downsides: If the plunger fails, you need a toilet
Some sources recommend pouring bleach followed by hot water. This is dangerous. Hot water degrades sodium hypochlorite into oxygen gas and salt, releasing toxic chlorine gas fumes. More importantly, hot water can crack porcelain toilet bowls due to thermal shock. This combination provides no unblocking benefit. If the plunger fails