I share the same desire to study abroad.

Literal

Study-abroad want [quotative-という] feeling [topic-は] I [also-も] same-way [adverbial-に] have.

~という気持ちは僕も同じように持っている — 'I too hold the same feeling of wanting to study abroad.' The construction is somewhat formal/deliberate — explicitly stating shared feelings rather than simply saying 僕も留学したい.