Validity of formulas

Question

So i know that if $(∃x ϕ)$ is valid that doesnt implie that doesnt implie that $ (∀x ϕ) $ is also valid, my question is if it is sufficient for me to get an interpretation stucture that satisfies the first and doesnt satisfy the second or i actually need to find a formula that works for every interpretation stucture and then show it doesnt satisfy the second, because it doesnt seem so easy to get that formula.