James -
My guess is that there's still an error in the model number listed here, as it doesn't come up as-is with Sears. I have a dryer that appears to be just like that one, and it's number is 110.76860100.
I'm thinking that there is tranposition or a difficult to read digit in the number that Toggleswitch supplied. I might bet a couple bucks that the model number is 110.76960130.
Here is my rationale: My model number catalog from Whirlpool lists three essentially similar dryers, all that use the black and woodgrain console, and the same 4-cycle timer (which is not set-up for automatic thermostat or moisture sensing drying). One is a 76 model, the second a 78 which I have and the third a 79. The '79 is the only one that had any mechanical revisions, which is what the "30" means at the end of the number. The '79 had in fact three revisions and 110.76960130 is a good model number. I think Toggle got a couple digits transposed.
If so, that means he has a 1979 model dryer. That model, having so many revisions, may have survived in production well into 1980 or 1981.