Police went to the home near 4900 South and 1000 East around 5 p.m. after dispatchers reported receiving a 911 hang-up call.
At the home, an 11-year-old girl carrying a baby answered the door but was hesitant to allow deputies inside.
"She really didn't want us to see the house," said Lt. Paul Jaroscak, a Salt Lake County Sheriff's Office spokesman. "It seemed like she was struggling emotionally."
The girl said 11 children lived in the house, ranging from 9 months to 17 years of age, and that her mother was at work.
Police found dirty dishes and spoiled food in the kitchen and pet feces and a strong urine smell throughout the house.
"There was literally a pathway of dirty clothes that they had to go through from room to room," Jaroscak said.
Grace Mitchell, the children's mother, arrived home and told police that "things were just a little dirty right now" and that the home's condition wasn't usually "that bad," Jaroscak said.
She also told police that Paul Kingston, the children's father, had not been home for several months.
A family member told The Salt Lake Tribune that a child in the home apparently was trying to call Mitchell's cell phone, which begins with the digit 9, but misdialed.
Kingston is the leader of the Davis County Cooperative Society, which has about 1,500 members in the Salt Lake Valley.
His brother John Daniel Kingston and plural wife Heidi Mattingly Foster were involved in a protracted, three-year child welfare case, which was closed in December 2006. The case, which began as a dispute between the parents and two daughters over ear piercing, included similar allegations of substandard living conditions.
It led the Davis County Cooperative Society to form a housekeeping inspection team - called Homemakers of Zion - aimed at preventing allegations such as those now being made about Mitchell's home. The Salt Lake County Sheriff's Office and the Division of Child and Family Services said Friday they are continuing to investigate the situation.
"The case is open, [but] we have not removed the children," said Carol Sisco, DCFS spokeswoman. "We'll probably be providing some services in the home to the mom."
Jaroscak said charges of child neglect and endangerment are possible and that the case may be referred to the District Attorney's Office.