--description--

A triplet of positive integers ($a$,$b$,$c$) is called a Cardano Triplet if it satisfies the condition:

$$\sqrt[3]{a + b \sqrt{c}} + \sqrt[3]{a - b \sqrt{c}} = 1$$

For example, (2,1,5) is a Cardano Triplet.

There exist 149 Cardano Triplets for which $a + b + c ≤ 1000$.

Find how many Cardano Triplets exist such that $a + b + c ≤ 110\,000\,000$.

--hints--

cardanoTriplets() should return 18946051.

assert.strictEqual(cardanoTriplets(), 18946051);

--seed--

--seed-contents--

function cardanoTriplets() {

  return true;
}

cardanoTriplets();

--solutions--

// solution required