[math-fun] Mathologer cubic messup?

https://www.youtube.com/watch?v=N-KXStupwsc offers an attractive expression for (one) solution of the general cubic, but I can't make it work. Have I entered this incorrectly? In[488]:= Power[#1 - Sqrt[#1^2 + #2^3], (3)^-1] + Power[#1 + Sqrt[#1^2 + #2^3], (3)^-1] - b/3/a &[-b^3/27/a^3 + b c/6/a/a - d/2/a, c/3/a - b^2/9/a/a] Out[488]= -(b/(3 a)) + (-(b^3/(27 a^3)) + (b c)/(6 a^2) - d/(2 a) - Sqrt[(-(b^2/(9 a^2)) + c/(3 a))^3 + (-(b^3/(27 a^3)) + (b c)/( 6 a^2) - d/(2 a))^2])^( 1/3) + (-(b^3/(27 a^3)) + (b c)/(6 a^2) - d/(2 a) + Sqrt[(-(b^2/(9 a^2)) + c/(3 a))^3 + (-(b^3/(27 a^3)) + (b c)/( 6 a^2) - d/(2 a))^2])^(1/3) —rwg