Kann keine or kann nicht?
What is the difference between Ich kann keine sechzig Kilometer laufen And Ich kann nicht sechzig Kilometer laufen? Why we use keine?why not kein?
Without context, I'd prefer "keine". The connotation there is, as tiramisues said, that it's a general rule that this amount of km is too much for me to handle, because I can only walk for 20 km and then I'm exhausted.
I'd use "nicht" in a context like this: "Ich kann nicht 60 km zu meiner Tante laufen, wenn ich für die Prüfung lernen sollte." "I can't walk 60 km to [visit] my aunt when I should be studying for the exam." = I could physically walk that distance, it's just that I don't have the time.
"Ich kann doch nicht 60 km laufen!" - You/they can't expect me to walk a 60 km distance! (e.g. as an answer to: "Our venue is located in Lower Smallhovel. The nearest train station is in Uptown (60 km)." or "Instead of complaining about the lack of parking spaces at the festival, you could use your feet for once and just walk there.")
Or maybe: "Ich kann nicht einfach 60 km laufen!" - I can't just/simply walk 60 km, it's more "complicated" than that (e.g. I need my hiking shoes, I need to take the day off at work first)