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Given:
$a+b+c-3(abc)^\dfrac{1}{3}=0$...............................................................(1)
$\neg((a)^\dfrac{1}{3}=(b)^\dfrac{1}{3}) $ ........................................(2)
$\neg((b)^\dfrac{1}{3}=(c)^\dfrac{1}{3})$ ........................................(3)
$\neg((c)^\dfrac{1}{3}=(a)^\dfrac{1}{3})$............................................(4)
Then prove:
$(a)^\dfrac{1}{3}+(b)^\dfrac{1}{3}+(c)^\dfrac{1}{3}=0$