Sludge/dirt is spinning back into the inner basket/basin from the top perforated holes into the inner spin basket during drain cycle. Water is not draining well out of clothes. The sludge/dirt smells foul. Light grey in color.

When this problem began, the washing machine did start to sound a bit different -- a duller sound -- and there was a very minute burning smell.

My guess is that there is a clog? How do I check for an item that may be creating a clog? Or other possible culprits?

I did open up the machine and removed the pump to see if there was something in the plastic pipes. The water that drained out from both pipes smelled foul, but I could not see anything stuck inside. I don't know how to look anywhere else.

Kenmore top load clothes washer, model 11918812700

Thank you for any and all advice.

dmez,
Good question - first your model number is 11018812700 or it should be the 110- units are built by whirlpool 119# is a stove. I digress!
Possible solution: Today detergents and fabric softeners (especially ones that are HE) at times may not completely dissolve and adhere to the plastic outer drum. Then with subsequent washings more build up occurs along with the entrapment of dirt from the wash cycle. If this continues for a long time the dirt(some being organic) in the "sludge " becomes foul and also can hamper water drainage etc.
Try running "AttFresh" through a large (water) load using longest cycle with hot/warm water. This will dissolve the sludge and be pumped out during drain and spin. With a large build up it may take two or three cleanings.
Hope this helps......

Great, glad you found that and got it fixed, and thanks for updating us.