Obviously, a book with a copyright date of 1935 could not have been printed before that date, but it may have been printed after that date.
At that time (no longer), a copyright was for 28 years and could be renewed once. The 1935 date probably applies to the renewal. You may find that the edition you have includes information such as "First printing," "Second printing" which may give an insight into when that particular book was made.
Generally, what makes a book valuable are its importance and its condition. A first edition is almost always the most collectable and thus most valuable.
A first edition of something by, say, Mark Twain or Ernest Hemingway (particularly of their most significant works) would almost surely have more value than a first edition of "The Autobiography of Joe Schlub." Nobody cares about Joe Schlub.
Most collectors want only books in perfect condition, including the dust jacket (in perfect condition also). This would not apply to very rare and significant books.
"Anne of Green Gables" has perhaps millions of volumes in print, which means it is not rare. Since yours is not a first edition, it is unlikely to have much monetary value.