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?
I think the difference is that if you can't eat vegetables, there's not really any difference between being unable to eat any vegetables, or vegetables as a general rule:
Ich kann kein Gemüse essen. Ich kann Gemüse nicht essen. = I can't eat vegetables. As usual, you can think of "kein" as "not any", "no"; while "nicht" is a simple negation and more universal-sounding.
Some more obvious examples:
Ich kann keine Vögel sehen. = I can't see any birds.
Ich kann die Vögel nicht sehen. = I can't see the birds.
Ich kann Vögel nicht sehen. = I can't see birds. = I have a strange superpower that makes all birds invisible to my eyes.
Ich kann keine zehn Vögel sehen. = I can't see as many as ten birds. / I can't see those "ten birds" that I'm supposed to see.
Ich kann die zehn Vögel nicht sehen. = I can't see those ten birds you were talking about.
Ich kann zehn Vögel nicht sehen. = There are ten birds I can't see. = There's a "Find Waldo" kind of picture with 100 birds on it, but I can only find 90.
Ich kenne keine Franzosen. = I don't know any Frenchmen.
Ich kenne die Franzosen nicht. = I don't know the French. / I don't know those Frenchmen.
Ich kenne Franzosen nicht. = I have never heard about such a thing as Frenchmen.
Ich kenne keine zehn Franzosen. = I don't know as many as ten Frenchmen. / I don't know those "ten Frenchmen" you claim to have seen me with yesterday.
Ich kenne die zehn Franzosen nicht. = I don't know those ten Frenchmen.
Ich kenne zehn Franzosen nicht. = There are ten Frenchmen I don't know.
Ich kenne Franzosen. I know (some) Frenchmen.
Ich kenne die Franzosen. I know the French. / I know those Frenchmen.
Ich kenne zehn Franzosen. I know ten Frenchmen.
Ich kenne die zehn Franzosen. I know those ten Frenchmen.
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)