The International Agency for Research on Cancer identified a possible link between aspartame and a type of liver cancer called hepatocellular carcinoma.
According to WHO, 40mg per kg of body weight is the safe limit.
Concentration of aspartame in chewing gum samples was between 1.9 and 30.5 μg/g with an average of 11.1 μg/g
So on average, 3.6kg of chewing gum contains 40mg of aspartame.
An average human weights around 60kg. So an average human would be within safe limit by chewing 216kg of gum a day. That's about 475 pounds of gum a day.