Qual è la differenza tra negara e negeri ?Sentiti libero di rispondere con un esempio.

"Negara" is different from "Negeri", just so you know. Negara means country, while negeri is like "the land", though it's not entirely like that.

"Indonesia is a country full of local cultures." -> The "country" here means "negara".

"Indonesia is a land of cultures." -> The "land" here is "negeri".
While in this sentence:
"Apa yang membuat kamu ingin belajar di luar negeri?", there's a fixed phrase, "luar negeri", which is quite different in meaning if you translate each word instead of the whole phrase. "Luar negeri" means "overseas", making "negeri" itself a different meaning, but there's still a faint idea of "land". If separately translated, "luar negeri" means "outside the land", barely similar to "overseas".
And it also applies to the phrase, "dalam negeri", meaning domestic". If separately translated, it will become "inside the land".
Another example:
"In the 2nd century, China was known as The Land of Three Kingdoms — Shu, Wu, and Wei, storied kingdoms in their era." with "The Land of Three Kingdoms" meaning "Negeri Tiga Kerajaan".

Negeri and Negara have never been the same in meaning, while somewhat close to each other.