It's a 1967 model. It could have been made in 1966 but "L" designates 1967 Frigidaire models ("K" is for 1966, "J" is for 1965, "N" is for 1968, "P" is for 1969, "R" for 1970...). Many models were produced for a few years and skipped some model year letters but not 40" "L" series free-standing ranges which were produced around mid-1966/mid-1967 (just like cars). I don't have many parts for these but if you find what you need to replace, I could provide you the part numbers to search for. Replacement burners are still easy to get but they are usually not the first thing to go wrong.
Can you describe more precisely what's wrong with your range. Which burner doesn't work, does the faulty burner's switch turns-on and off the pilot light? And how about the oven? Does it stay cool when you turn it on or it just doesn't shuts off at the correct temperature? Does the broil element work? Is it the self-cleaning side that's not working or the small oven? Do the pilot lights for the broil and bake elements turn on? Is the clock/timer (Meal Minder on this model) still working? How is it set?
Then, if you're used to work on electrical appliances, you can disconnect the power and test circuits with an ohmmeter. There should be a wiring diagram at the back of the range to help you figure which wire goes where.
Sometimes, it's also possible to replace parts with different part numbers. Just a few days ago, I replaced the oven thermostat for my 1968 model (1969 production) RBE-539N Compact 30 Electri-Clean range and I used parts from a 1973 Electri-Clean wall oven thermostat combined with mine and it works. The Speed Heat burner switch was also bad so I combined parts from my bad switch and a 1960 cooktop Speed Heat switch and it also works fine.