I have asked about moving a tick mark from below the x-axis to above the x-axis. (I used the specification xticklabel shift=-16pt.) In the following graph, the tick mark is at a point where the graph has a horizontal asymptote. I need to move the tick mark 2pt either to the left or to the right.

\documentclass[10pt]{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}
\begin{axis}[width=6in,axis equal image,unit vector ratio={2 1},clip=false,
axis lines=middle,
xmin=-1.5,xmax=2.5,
domain=-1.5:2.5, samples=201,
xlabel=$x$,ylabel=$y$,
ymin=-1,ymax=3,
restrict y to domain=-1:3,
enlargelimits={abs=0.5cm},
axis line style={latex-latex},
ticklabel style={font=\tiny,fill=white},
xtick={\empty},ytick={\empty},
extra x ticks={0.83333, 1, 1.6666},
extra x tick labels={$\frac{5}{6}$, $1$, $\frac{5}{3}$},
extra y ticks={-2},
extra y tick labels={$ma+b$},
yticklabel style={anchor=west},
yticklabel shift=-4pt,
ticklabel style={font=\tiny,fill=white},
xtick={0.83333, 1, 1.6666},ytick={\empty},
xlabel style={at={(ticklabel* cs:1)},anchor=north west},
ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]
\addplot[samples=501,domain=-1.5:1,blue] {-1* x * abs((x - 1))^(1/5)};
\addplot[samples=501,domain=1:4,blue] {x * abs((x - 1))^(1/5)} node[below right,pos=0.75,font=\footnotesize]{$y=f(x)$};
\draw [fill] (0.83333,-0.58236) circle [radius=1.5pt];
\draw [fill] (1,0) circle [radius=1.5pt];
\draw [fill] (1.6666,1.53685) circle [radius=1.5pt];
\end{axis}
\end{tikzpicture}
\end{document}

ticklabel style={xshift=2pt,font=\tiny,fill=white},Note xshift. If you want it only forxticks, use a separatexticklabel style– Oct 30 '14 at 01:00