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The 21-year-old, who is currently studying for a degree at the University of Alabama in the United States, came through qualifying at Woburn after carding back-to-back rounds of 67 to finish on 10 under par.
Three spots were available at each of the four venues hosting qualifying ahead of the tournament at Hoylake.
Dunne almost missed the chance to qualify for the upcoming Open after arriving on the first tee at Woburn with just a minute to spare ahead of his opening round.
Luckily he quickly recovered from the fright to hit some impressive shots and book his place among golf's elite.
European Tour professional Oliver Fisher came second on seven under while Welshman Rhys Enoch won a tense three-man play-off to claim the final place.
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