What if triangle does not exist with the given sides? Maybe add an appropriate test case aka "not exist"?

Add test cases: start with opening bracket.

Expect(ValidMixedBracketsParentheses(")(")).To(Equal(false))
Expect(ValidMixedBracketsParentheses("}{")).To(Equal(false))
Expect(ValidMixedBracketsParentheses("][")).To(Equal(false))

Add test cases: mixed bracket types.

Expect(ValidMixedBracketsParentheses("(}")).To(Equal(false))
Expect(ValidMixedBracketsParentheses("{)")).To(Equal(false))
Expect(ValidMixedBracketsParentheses("[)")).To(Equal(false))

Comparing values is not a novel or interesting idea, and IIRC there's already a kata with an exact same task as well.

Needs more (random) tests

No random tests

This is a duplicate to many katas.