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The moment I see your question my gut feeling tells me there must be no trivial solution. I searched on the Mathworld page of

Diophantine Equation -- 3rd Powers

and found the reference paper

J.C.P. Miller & M.F.C. Woollett, Solutions of the Diophantine equation x3 + y3 + z3 = k, J. London Math. Soc. 30 (1955), 101–110.

There are two other articles reference the same source.

• Rowland, Known Families of Integer Solutions of x3 + y3 + z3 = n
• Heath-Brown, On Solving The Diophantine Equation X3 +Y3 +Z3 = K On A Vector Computer

In your case, there is no known solution yet according to Heath-Brown. Mathematica can found the following solution with some hint:

In[5]:= Reduce[a^3+b^3+(-159380)^3==39,{a,b},Integers]
Out[5]= (a==117367&&b==134476)||(a==134476&&b==117367)