I am looking for some (may be rarely know to nonnative English speakers) synonyms for "immensely valuable" or "extremely valuable".
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The word "invaluable" is what you're looking for I think. Definition: beyond calculable or appraisable value.
There are also the terms precious, which means "of great price; costly; having a high money-value; of great worth; held in high esteem; intrinsically valuable," and inestimable, which means "of immeasurable value or worth; invaluable."