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> How to show that $$\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3?$$
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This equality comes from solving $$t^3 - 15 t - 4 = 0$$ using [Cardanos fomula](https://proofwiki.org/wiki/Cardano%27s_Formula]) and knowing the solution $t\_1=4$.

I have attempted multiplying the whole thing with $(\sqrt[3]{18+5\sqrt{13}})^2 - (\sqrt[3]{18-5\sqrt{13}})^2$, but no success. Then I have solved for one cubic root and put all to the third power. Also no success.